Existence and Uniqueness of Local Regular Solution to the Schrodinger Flow from a Bounded Domain in R3 into S2

作者：Chen, Bo^*; Wang, Youde

来源：Communications in Mathematical Physics, 2023, 402(1): 391-428.

DOI：10.1007/s00220-023-04730-9

• SELF-SIMILAR SOLUTIONS
• GLOBAL WELL-POSEDNESS
• WEAK SOLUTIONS
• MAPS
• SYSTEM
• SPACE

In this paper, we show the existence and uniqueness of local regular solutions to the initial-Neumann boundary value problem of the Schrodinger flow from a smooth bounded domain O ? R-3 into S-2(namely Landau-Lifshitz equation without dissipation). The proof is built on a parabolic perturbation method, an intrinsic geometric energy argument, the symmetric (algebraic) properties of S(2 )and some observations on the behaviors of some geometric quantities on the boundary of the domain manifold. It is based on methods from Ding and Wang (one of the authors of this paper) for the Schrodinger flows of maps from a closed Riemannian manifold into a Kahler manifold as well as on methods by Carbou and Jizzini for solutions of the Landau-Lifshitz equation.

• 单位
  广州大学